Pricing American options under variance gamma

Ali Hirsa, Dilip B. Madan

Abstract

ABSTRACT

We derive partial integro-differential equations (PIDE) for pricing American options when the log price dynamics of the underlying asset is given by the variance gamma (VG) law. A numerical algorithm for pricing American options under this law is then presented. A comparison of exercise boundaries and early exercise premia, between geometric VG laws and geometric Brownian motion (GBM), reveals that GBM American option premia understate the corresponding VG premia. We are thereby led to conclude that further work is necessary to develop fast, efficient algorithms for solving PIDEs with a view to synthesizing stochastic processes to a surface of American option prices.